Question Video: Using the Properties of Parallelograms to Solve a Problem

Video Transcript

Find the lengths of line 𝐶𝐷 and line 𝐷𝐴.

First, we’re interested in line 𝐶𝐷 and, second, line 𝐷𝐴. Before we can determine the lengths of these lines, we need to think about what we know about this figure. Line 𝐷𝐴 is parallel to line 𝐶𝐵. And line 𝐷𝐶 is parallel to line 𝐴𝐵. This tells us that in this shape, opposite sides are parallel. And so we can say that 𝐴𝐵𝐶𝐷 is a parallelogram. And in a parallelogram, opposite sides are equal in length. Line 𝐷𝐶 is opposite line 𝐴𝐵. And therefore, 𝐷𝐶 and 𝐴𝐵 are equal in length. If 𝐷𝐶 equals 𝐴𝐵, then they both measure 15 centimeters. We can also say that line 𝐴𝐷 is opposite line 𝐵𝐶 which makes line 𝐴𝐷 equal to line 𝐵𝐶 and a measure of 13 centimeters. 𝐶𝐷 equals 15 centimeters and 𝐴𝐷 equals 13 centimeters. Notice that we can write the name of the line with the end points in either order. 𝐷𝐴 and 𝐴𝐷 are the same lines, and 𝐶𝐷 and 𝐷𝐶 are also the same lines.